Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4....

Imagine you consume two goods, X and Y, and your utility function is U = X^1/2Y^1/4. Your budget is M = 630; PX = $10; PY = $30. Now imagine PX increases to $25. The compensated price bundle is (30.9458, 12.8941). What is the income effect on X?

Solutions

Expert Solution

U=X^(1/2) Y^(1/4)

MRS= -MUx/MUy= -(0.5/0.25)(y/x)= -2y/x

New Budget line Equation:

25X+30Y= 630

-Px/Py= -25/30= -5/6

At equilibrium

MRS=Px/Py

-2y/x=-5/6

12y=10x

1.2y=x

25*1.2y+30y=630

60y=630

y*= 10.5

x*= 1.2*10.5= 12.6

New demand for good x= 12.6

Compensated demand for good x= 30.9458

Income effect= compensated demand- New demand= 18.3458

Income effect on good x= 18.3458

Rahul Sunny answered 1 year ago

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